Problem: Simplify the following expression: $ a = \dfrac{x + 1}{-9} - \dfrac{-7}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{x + 1}{-9} \times \dfrac{2}{2} = \dfrac{2x + 2}{-18} $ Multiply the second expression by $\dfrac{-9}{-9}$ $ \dfrac{-7}{2} \times \dfrac{-9}{-9} = \dfrac{63}{-18} $ Therefore $ a = \dfrac{2x + 2}{-18} - \dfrac{63}{-18} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{2x + 2 - 63 }{-18} $ Distribute the negative sign: $a = \dfrac{2x + 2 - 63}{-18}$ $a = \dfrac{2x - 61}{-18}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-2x + 61}{18}$